For the function f given above, determine whether the following conditions are true. Input T if the condition is true, otherwise input F . (a) f'(x)2; (c) f''(x)

Question

For the function f given above, determine whether the following conditions are true. Input T if the condition is true, otherwise input F . (a) f'(x)<0 0 if x>2; (c) f''(x)<0 if 0<=x<1; (d) f''(x)>0 if 14; (f) Two inflection points of f(x) are, the smaller one is x= and the other is x=

anonymous · Answer

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agent0smith · Answer

For f'(x), just look at the slope in those regions.

For f''(x), look at the concavity.

anonymous · Answer

alright give me a moment

agent0smith · Answer

The hardest part is (f) Two inflection points of f(x) are, the smaller one is x= and the other is x= you'll just have to estimate where they are, it's hard to say exactly. Look for a point where concavity changes http://derivative-functions.cours-de-math.eu/inflection-point.GIF (I have no idea why the concavite appears to be in french, and everything else is in english) :P

anonymous · Answer

so for my answers i got t,f,t,t,t do you think its correct and for the inflection points im not really sure but i think one of them might be 1 and the other probably 4

anonymous · Answer

yeah i just checked they are correct thank you :)

agent0smith · Answer

I didn't check them, but good job finding x=1 and x=4 for the inflection points - those were my estimates too :)

anonymous · Answer

thanks again and good night :)

agent0smith · Answer

You're welcome :)